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Mainframe sort merge IBM OS/VS SORT Mainframe_sort_merge > IBM OS/VS SORT The distribution techniques listed for tape sorts were retained by the OS/VS SORT program, now called "conventional techniques." The disk sort techniques were replaced by four new ones: FLR-Blockset for fixed length records VLR-Blockset for variable-length records Peerage for fixed length records Vale for both fixed and variable-length records
Mathematical symmetry Examples Mathematical_symmetry > Symmetry in abstract algebra > Automorphisms of algebraic objects > Examples In set theory, an arbitrary permutation of the elements of a set X is an automorphism. The automorphism group of X is also called the symmetric group on X. In elementary arithmetic, the set of integers, Z, considered as a group under addition, has a unique nontrivial automorphism: negation. Considered as a ring, however, it has only the trivial automorphism. Generally speaking, negation is an automorphism of any abelian group, but not of a ring or field.
Monoamine transporter Depression Monoamine_transporter > Associated disorders and treatments > Depression Therefore, drugs such as venlafaxine and paroxetine are being used as effective antidepressants that selectively inhibit both SERT and NET. The tricyclic antidepressant desipramine is an antidepressant drug that is a relatively selective inhibitor of NE uptake. Studies of inhibition of NET correlate with antidepressant activity.
Biological clock (aging) Cellular senescence versus epigenetic aging Epigenetics_of_aging > Applications of Horvath's clock > Cellular senescence versus epigenetic aging Consistent with this, telomerase-immortalised cells continued to age (according to the epigenetic clock) without having been treated with any senescence inducers or DNA-damaging agents, re-affirming the independence of the process of epigenetic ageing from telomeres, cellular senescence, and the DNA damage response pathway. Although the uncoupling of senescence from cellular aging appears at first sight to be inconsistent with the fact that senescent cells contribute to the physical manifestation of organism ageing, as demonstrated by Baker et al., where removal of senescent cells slowed down aging.The epigenetic clock analysis of senescence, however, suggests that cellular senescence is a state that cells are forced into as a result of external pressures such as DNA damage, ectopic oncogene expression and exhaustive proliferation of cells to replenish those eliminated by external/environmental factors. These senescent cells, in sufficient numbers, will probably cause the deterioration of tissues, which is interpreted as organism ageing.
Three-spool engine Principles Turbofan_engines > Principles Firstly, energy is wasted as the propelling jet is going much faster rearwards than the aircraft is going forwards, leaving a very fast wake. This wake contains kinetic energy that reflects the fuel used to produce it, rather than the fuel used to move the aircraft forwards. A turbofan harvests that wasted velocity and uses it to power a ducted fan that blows air in bypass channels around the rest of the turbine.
Thoralf Skolem Mathematics Thoralf_Skolem > Mathematics Skolem (1922) refined Zermelo's axioms for set theory by replacing Zermelo's vague notion of a "definite" property with any property that can be coded in first-order logic. The resulting axiom is now part of the standard axioms of set theory. Skolem also pointed out that a consequence of the Löwenheim–Skolem theorem is what is now known as Skolem's paradox: If Zermelo's axioms are consistent, then they must be satisfiable within a countable domain, even though they prove the existence of uncountable sets.
Hexagram Other symbolic uses Hexagram > Other uses > Other symbolic uses The Indian sage and seer Sri Aurobindo used it—e.g. on the cover of his books—as a symbol of the aspiration of humanity calling to the Divine to descend into life (the triangle with the point at the top), and the descent of the Divine into the earth's atmosphere and all individuals in response to that calling (the triangle with the point at the bottom). (This was explained by the Mother, his spiritual partner in Her 14-volume Agenda and elsewhere by Sri Aurobindo in his writings.)
Pressure Fluid pressure Fluid_pressure > Types > Fluid pressure Such conditions conform with principles of fluid statics. The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure. Closed bodies of fluid are either "static", when the fluid is not moving, or "dynamic", when the fluid can move as in either a pipe or by compressing an air gap in a closed container.
Glossary of systems theory R Glossary_of_systems_theory > R Reductionism: One kind of scientific orientation that seeks to understand phenomena by a) breaking them down into their smallest possible parts (a process known as analytic reductionism), or conversely b) conflating them to a one-dimensional totality (a process known as holistic reductionism).
Finite element method in structural mechanics Interpolation or shape functions Finite_element_method_in_structural_mechanics > Interpolation or shape functions Let q {\displaystyle \mathbf {q} } be the vector of nodal displacements of a typical element. The displacements at any other point of the element may be found by the use of interpolation functions as, symbolically: where u {\displaystyle \mathbf {u} } = vector of displacements at any point {x,y,z} of the element. N {\displaystyle \mathbf {N} } = matrix of shape functions serving as interpolation functions.Equation (6) gives rise to other quantities of great interest: Virtual displacements that are a function of virtual nodal displacements: Strains in the elements that result from displacements of the element's nodes: where D {\displaystyle \mathbf {D} } = matrix of differential operators that convert displacements to strains using linear elasticity theory. Eq.(7) shows that matrix B in (4) is Virtual strains consistent with element's virtual nodal displacements:
Stability derivatives Linearization (simplification) of stability analysis Stability_derivatives > Uses > Linearization (simplification) of stability analysis Stability and control derivatives change as flight conditions change. That is, the forces and moments on the vehicle are seldom simple (linear) functions of its states. Because of this, the dynamics of atmospheric flight vehicles can be difficult to analyze. The following are two methods used to tackle this complexity.
Marine habitat Coastal Marine_environment > Coastal Tides do not typically cause erosion by themselves; however, tidal bores can erode as the waves surge up river estuaries from the ocean. Waves erode coastline as they break on shore releasing their energy; the larger the wave the more energy it releases and the more sediment it moves. Sediment deposited by waves comes from eroded cliff faces and is moved along the coastline by the waves.
Major trauma Pathophysiology Major_trauma > Pathophysiology Prolonged inflammation may cause multiple organ dysfunction syndrome or systemic inflammatory response syndrome. Immediately after injury, the body increases production of glucose through gluconeogenesis and its consumption of fat via lipolysis. Next, the body tries to replenish its energy stores of glucose and protein via anabolism. In this state the body will temporarily increase its maximum expenditure for the purpose of healing injured cells.
Psi-theory Perception Psi-theory > Main assumptions > Perception Perception is based on conceptual hypotheses, which guide the recognition of objects, situations and episodes. Hypothesis based perception ("HyPercept") is understood as a bottom-up (data-driven and context-dependent) cuing of hypotheses that is interleaved with a top-down verification. The acquisition of schematic hierarchical descriptions and their gradual adaptation and revision can be described as assimilation and accommodation. Hypothesis based perception is a universal principle that applies to visual perception, auditory perception, discourse interpretation and even memory interpretation. Perception is subject to emotional modulation.
Inner core Dynamics Inner_core > Dynamics Because the inner core is not rigidly connected to the Earth's solid mantle, the possibility that it rotates slightly more quickly or slowly than the rest of Earth has long been entertained. In the 1990s, seismologists made various claims about detecting this kind of super-rotation by observing changes in the characteristics of seismic waves passing through the inner core over several decades, using the aforementioned property that it transmits waves more quickly in some directions. In 1996, X. Song and P. Richards estimated this "super-rotation" of the inner core relative to the mantle as about one degree per year. In 2005, they and J. Zhang compared recordings of "seismic doublets" (recordings by the same station of earthquakes occurring in the same location on the opposite side of the Earth, years apart), and revised that estimate to 0.3 to 0.5 degree per year.
T cell receptor Antigen discrimination T-cell_receptor > Antigen discrimination Nevertheless, the T-cell receptor signalling should not be activated by self-pMHC so that endogenous, healthy cells are ignored by T cells. However, when these very same cells contain even minute quantities of pathogen-derived pMHC, T cells must get activated and initiate immune responses. The ability of T cells to ignore healthy cells but respond when these same cells express a small number of foreign pMHCs is known as antigen discrimination.To do so, T cells have a very high degree of antigen specificity, despite the fact that the affinity to the peptide/MHC ligand is rather low in comparison to other receptor types.
Protofection Summary Protofection Protofection is a protein-mediated transfection of foreign mitochondrial DNA (mtDNA) into the mitochondria of cells in a tissue to supplement or replace the native mitochondrial DNA already present. The complete mtDNA genome or just fragments of mtDNA generated by polymerase chain reaction can be transferred into the target mitochondria through the technique.Scientists have hypothesized for the last couple of decades that protofection can be beneficial for patients with mitochondrial diseases. This technique is a recent development and is continuously being improved. As mitochondrial DNA becomes progressively more damaged with age, this may provide a method of at least partially rejuvenating mitochondria in old tissue, restoring them to their original, youthful function.
Supramolecular catalysis Stabilizing transition state Supramolecular_catalysis > Mechanism of catalysis > Stabilizing transition state A Diels Alder reaction between two pyridine functionalized substrates normally yield a mixture of endo and exo products. In the presence of the two catalysts, however, complete endo selectivity or exo selectivity could be obtained. The underlying cause of the selectivity is the coordination interaction between pyridine and the zinc ion on porphyrin. Depending on the shape of the catalysts, one product is preferred over the other.
Spectral element method Discussion Spectral_element_method > Discussion In SEM computational error decreases exponentially as the order of approximating polynomial increases, therefore a fast convergence of solution to the exact solution is realized with fewer degrees of freedom of the structure in comparison with FEM. In structural health monitoring, FEM can be used for detecting large flaws in a structure, but as the size of the flaw is reduced there is a need to use a high-frequency wave. In order to simulate the propagation of a high-frequency wave, the FEM mesh required is very fine resulting in increased computational time.
Contact metamorphic Equilibrium mineral assemblages Contact_metamorphic > Equilibrium mineral assemblages A reaction will begin at the temperature and pressure where the Gibbs free energy of the reagents becomes greater than that of the products.A mineral phase will generally be more stable if it has a lower internal energy, reflecting tighter binding between its atoms. Phases with a higher density (expressed as a lower molar volume V) are more stable at higher pressure, while minerals with a less ordered structure (expressed as a higher entropy S) are favored at high temperature. Thus andalusite is stable only at low pressure, since it has the lowest density of any aluminium silicate polymorph, while sillimanite is the stable form at higher temperatures, since it has the least ordered structure.The Gibbs free energy of a particular mineral at a specified temperature and pressure can be expressed by various analytic formulas.
Introduction to gauge theory Quantum electrodynamics Introduction_to_gauge_theory > In quantum mechanics > Quantum electrodynamics Until the advent of quantum mechanics, the only well known example of gauge symmetry was in electromagnetism, and the general significance of the concept was not fully understood. For example, it was not clear whether it was the fields E and B or the potentials V and A that were the fundamental quantities; if the former, then the gauge transformations could be considered as nothing more than a mathematical trick.
Glucocorticoid Withdrawal Glucocorticoid > Side effects > Withdrawal In addition to the effects listed above, use of high-dose glucocorticoids for only a few days begins to produce suppression of the patient's adrenal glands suppressing hypothalamic corticotropin-releasing hormone (CRH) leading to suppressed production of adrenocorticotropic hormone (ACTH) by the anterior pituitary. With prolonged suppression, the adrenal glands atrophy (physically shrink), and can take months to recover full function after discontinuation of the exogenous glucocorticoid. During this recovery time, the patient is vulnerable to adrenal insufficiency during times of stress, such as illness. While suppressive dose and time for adrenal recovery vary widely, clinical guidelines have been devised to estimate potential adrenal suppression and recovery, to reduce risk to the patient.
Mobile signature roaming Entities involved Mobile_signature_roaming > Entities involved An Acquiring Entity implements the Web Service Interface specified in TS 102 204 ; Home MSSP (HMSSP): this is the MSSP that is able to deal with the current end-user and the current transaction; Routing Entity (RE): any entity that facilitates the communication between the AE and the home MSSP; Attribute Provider: this role is described by Liberty Alliance . One or several mesh members may undertake this role and store relevant attributes in order to facilitate the discovery of the Home MSSP by other Mesh members; Identity Issuer: an entity that is able to make a link between a Mobile Signature and an end user's identity. Within a PKI system, this is typically the certificate authority (CA) and/or a registration authority (RA); Verifying Entity (VE): an entity that can verify a Mobile Signature. A MSSP may be a Verifying Entity as well; Acquiring MSSP (AMSSP): this is a MSSP acting as an entry point in the Mesh. We can imagine that a commercial model for a mobile Signature Roaming Service is a Mesh of MSSPs which are fully or partially connected between each others.
Pollard's rho algorithm for logarithms Complexity Pollard's_rho_algorithm_for_logarithms > Complexity The running time is approximately O ( n ) {\displaystyle {\mathcal {O}}({\sqrt {n}})} . If used together with the Pohlig–Hellman algorithm, the running time of the combined algorithm is O ( p ) {\displaystyle {\mathcal {O}}({\sqrt {p}})} , where p {\displaystyle p} is the largest prime factor of n {\displaystyle n} .
Regulated function Properties of regulated functions Regulated_function > Properties of regulated functions This is not always equivalent with countability.The integral, as defined on step functions in the obvious way, extends naturally to Reg(; X) by defining the integral of a regulated function to be the limit of the integrals of any sequence of step functions converging uniformly to it. This extension is well-defined and satisfies all of the usual properties of an integral. In particular, the regulated integral is a bounded linear function from Reg(; X) to X; hence, in the case X = R, the integral is an element of the space that is dual to Reg(; R); agrees with the Riemann integral.
Kolmogorov's normability criterion Summary Kolmogorov's_normability_criterion In mathematics, Kolmogorov's normability criterion is a theorem that provides a necessary and sufficient condition for a topological vector space to be normable; that is, for the existence of a norm on the space that generates the given topology. The normability criterion can be seen as a result in same vein as the Nagata–Smirnov metrization theorem and Bing metrization theorem, which gives a necessary and sufficient condition for a topological space to be metrizable. The result was proved by the Russian mathematician Andrey Nikolayevich Kolmogorov in 1934.
Multidimensional discrete convolution Filtering on a helix Multidimensional_discrete_convolution > The helix transform > Filtering on a helix . . {\displaystyle h(n)=-1,0,...,0,-1,4,-1,0,...,0,-1,0,...} Notice in the one-dimensional filter that there are no leading zeroes as illustrated in the one-dimensional filtering strip after being unwound. The entire one-dimensional strip could have been convolved with; however, it is less computationally expensive to simply ignore the leading zeroes. In addition, none of these backside zero values will need to be stored in memory, preserving precious memory resources.
Ballistic conductivity Landauer–Büttiker formalism Ballistic_transport > Theory > Landauer–Büttiker formalism The contacts have a multiplicity of modes due to their larger size in comparison to the channel. Conversely, the quantum confinement in the 1D GNR channel constricts the number of modes to carrier degeneracy and restrictions from the energy dispersion relationship and the Brillouin zone. For example, electrons in carbon nanotubes have two intervalley modes and two spin modes.
Early life of Isaac Newton Birth and education Early_life_of_Isaac_Newton > Birth and education He formulated the three laws of motion: Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as sometimes indicated by their symbols being displayed in slant bold font); in this law, the direction of the force vector is the same as the direction of the acceleration vector. For every action there is an equal and opposite reaction.
Data plot Plots for specific quantities Data_plot > Types of plots > Plots for specific quantities It is a kind of recurrence plot. Lineweaver–Burk plot: This plot compares the reciprocals of reaction rate and substrate concentration. It is used to represent and determine enzyme kinetics.
Babylonian geometry Algebra Babylonian_geometry > Old Babylonian mathematics (2000–1600 BC) > Algebra They knew that a solution to this form of equation is: x = − b 2 + ( b 2 ) 2 + c {\displaystyle x=-{\frac {b}{2}}+{\sqrt {\left({\frac {b}{2}}\right)^{2}+c}}} and they found square roots efficiently using division and averaging. They always used the positive root because this made sense when solving "real" problems. Problems of this type included finding the dimensions of a rectangle given its area and the amount by which the length exceeds the width.
Rotary atomizers Working Principle Rotary_atomizers > Working Principle Rotary atomizers work on the principle of centrifugal energy; this energy is used to produce a high relative speed between the fluid and air which is essential for atomization. A rotary atomizer comprises a rotating surface. This surface can be in the form of a flat or a vaned disc, a cup, or a slotted wheel.
Simulation-based optimization Stochastic approximation Simulation-based_optimization > Simulation-based optimization methods > Stochastic approximation Stochastic approximation is used when the function cannot be computed directly, only estimated via noisy observations. In these scenarios, this method (or family of methods) looks for the extrema of these function. The objective function would be: min x ∈ θ f ( x ) = min x ∈ θ E {\displaystyle {\underset {{\text{x}}\in \theta }{\min }}f{\bigl (}{\text{x}}{\bigr )}={\underset {{\text{x}}\in \theta }{\min }}\mathrm {E} } y {\displaystyle y} is a random variable that represents the noise. x {\displaystyle x} is the parameter that minimizes f ( x ) {\displaystyle f{\bigl (}{\text{x}}{\bigr )}} . θ {\displaystyle \theta } is the domain of the parameter x {\displaystyle x} .
Congenital adrenal hyperplasia due to 21-hydroxylase deficiency Hormone replacement Congenital_adrenal_hyperplasia_due_to_21-hydroxylase_deficiency > Treatment > Long-term management of CAH > Hormone replacement (See Glucocorticoid for more on this topic.) However, the currently used glucocorticoid therapy methods may lead to unphysiological doses that, in addition to the problems caused by overexposure of androgens, can harm health.
Step cutting Summary Step_cutting Step cutting is a term used for a graduated haircut in which the hair takes the form of cascading steps. There is a sharp demarcation between the steps, which leads to the factor of having a "number of steps". A 2-step cut is where the shortest layer is above the shoulders and the next one a few inches below. The layers are made to curl out.Drastic variants of the cut can involve a very short first layer which is just below the ears. Doing this haircut is relatively easy — the hair is partitioned horizontally, and the lowest section serves as the guide.
Xeno Nucleic Acid Structure Xeno_Nucleic_Acid > Structure Strands of DNA and RNA are formed by stringing together long chains of molecules called nucleotides. A nucleotide is made up of three chemical components: a phosphate, a five-carbon sugar group (this can be either a deoxyribose sugar—which gives us the "D" in DNA—or a ribose sugar—the "R" in RNA), and one of five standard bases (adenine, guanine, cytosine, thymine or uracil). The molecules that piece together to form the six xeno nucleic acids are almost identical to those of DNA and RNA, with one exception: in XNA nucleotides, the deoxyribose and ribose sugar groups of DNA and RNA have been replaced with other chemical structures. These substitutions make XNAs functionally and structurally analogous to DNA and RNA despite being unnatural and artificial.
Period 1 element Position of period 1 elements in the periodic table Period_1_element > Position of period 1 elements in the periodic table It has some metal-like chemical properties, being able to displace some metals from their salts. But hydrogen forms a diatomic nonmetallic gas at standard conditions, unlike the alkali metals which are reactive solid metals. This and hydrogen's formation of hydrides, in which it gains an electron, brings it close to the properties of the halogens which do the same (though it is rarer for hydrogen to form H− than H+).
Rising film evaporator Overall rate of heat transfer Rising_film_evaporator > Main characteristic and assessments > Overall rate of heat transfer Considering that rising film evaporators use the same heat transfer principle as a general shell and tube heat exchanger. Therefore, the overall heat transfer rate is crucial in determining the performance of the evaporator. This factor will determine the capacity of the rising film evaporator. The fundamental general formula which gives the overall heat transfer rate is, where Q is the heat transfer Rate U is the overall heat transfer coefficient A is the overall heat transfer area Tlm is the temperature difference or log mean temperature differenceFor a general shell and tube heat exchanger, U is given by the equation where ho is the outside fluid film coefficient hi is the inside fluid film coefficient hod is the outside dirt coefficient (fouling factor) hid is the inside dirt coefficient kw is the thermal conductivity of the tube wall material di is the tube inside diameter do is the tube outside diameterA is given by the equation where N is the total number of tubes l is the length of the tubes do is the tube outside diameterThis is the contact area of heat transfer which involves the outer surface area of the long vertical tubes that are parallel and in direct contact with the heating media housed within the shell of the evaporator. The log mean temperature difference (LMTD), Tlm, is given by the equation where Thi is the hot fluid inlet temperature Tho is the hot fluid outlet temperature Tci is the cold fluid inlet temperature Tco is the cold fluid outlet temperatureThe hot fluid in the case of the rising film evaporator would be the steam in the shell side and the cold fluid would be the liquid inside the long tubes. In relation to the overall heat transfer rate, there are several key parameters that affect this characteristic specifically in terms of a rising film evaporator.
Java performance Startup time Java_performance > Comparison to other languages > Startup time Excelsior JET approaches the problem from the other side. Its Startup Optimizer reduces the amount of data that must be read from the disk on application startup, and makes the reads more sequential. In November 2004, Nailgun, a "client, protocol, and server for running Java programs from the command line without incurring the JVM startup overhead" was publicly released.
Pathology Renal pathology Pathology > General pathology > Anatomical pathology > Renal pathology Renal pathology is a subspecialty of anatomic pathology that deals with the diagnosis and characterization of disease of the kidneys. In a medical setting, renal pathologists work closely with nephrologists and transplant surgeons, who typically obtain diagnostic specimens via percutaneous renal biopsy. The renal pathologist must synthesize findings from traditional microscope histology, electron microscopy, and immunofluorescence to obtain a definitive diagnosis. Medical renal diseases may affect the glomerulus, the tubules and interstitium, the vessels, or a combination of these compartments.
Homologous protein Examples Enzyme_superfamilies > Examples α/β hydrolase superfamily Members share an α/β sheet, containing 8 strands connected by helices, with catalytic triad residues in the same order, activities include proteases, lipases, peroxidases, esterases, epoxide hydrolases and dehalogenases. Alkaline phosphatase superfamily Members share an αβα sandwich structure as well as performing common promiscuous reactions by a common mechanism. Globin superfamily Members share an 8-alpha helix globular globin fold.
Integral kinematics Strain absement Integral_kinematics > Strain absement Strain absement is the time-integral of strain, and is used extensively in mechanical systems and memsprings: a quantity called absement which allows mem-spring models to display hysteretic response in great abundance.
Essential discontinuity Rewriting Lebesgue's Theorem Classification_of_discontinuities > Rewriting Lebesgue's Theorem When I = {\displaystyle I=} and f {\displaystyle f} is a bounded function, it is well-known of the importance of the set D {\displaystyle D} in the regard of the Riemann integrability of f . {\displaystyle f.} In fact, Lebesgue's Theorem (also named Lebesgue-Vitali) theorem) states that f {\displaystyle f} is Riemann integrable on I = {\displaystyle I=} if and only if D {\displaystyle D} is a set with Lebesgue's measure zero. In this theorem seems that all type of discontinuities have the same weight on the obstruction that a bounded function f {\displaystyle f} be Riemann integrable on .
Essential discontinuity Rewriting Lebesgue's Theorem Classification_of_discontinuities > Rewriting Lebesgue's Theorem {\displaystyle .} Since countable sets are sets of Lebesgue's measure zero and a countable union of sets with Lebesgue's measure zero is still a set of Lebesgue's mesure zero, we are seeing now that this is not the case. In fact, the discontinuities in the set R ∪ J ∪ E 2 ∪ E 3 {\displaystyle R\cup J\cup E_{2}\cup E_{3}} are absolutely neutral in the regard of the Riemann integrability of f .
Biodegradable additives Anaerobic Biodegradable_additives > Mechanism of biodegradation > Indirect Action > Anaerobic Under anaerobic conditions, the lack of oxygen requires that the bacteria use a different source for an electron acceptor. Common electron acceptors used by anaerobic bacteria are sulfate, iron, nitrate, manganese and carbon dioxide. The resulting products under anaerobic conditions are carbon dioxide (CO2), water (H2O), and methane (CH4).A simple chemical equation of the anaerobic process is: C6H12O6 → 3CO2 + 3CH4Examples of anaerobic conditions for microbial biodegradation include soil and composts.
Presepsin Clinical relevance Presepsin > Clinical relevance Several clinical studies have demonstrated that presepsin is a specific and sensitive marker for the diagnosis, severity assessment and outcome prediction of sepsis. In addition, presepsin can be used for diagnosing infections in patients with a chronic inflammatory condition, such as liver cirrhosis. == References ==
Glycogenolysis Summary Glycogenolysis Glycogenolysis is the breakdown of glycogen (n) to glucose-1-phosphate and glycogen (n-1). Glycogen branches are catabolized by the sequential removal of glucose monomers via phosphorolysis, by the enzyme glycogen phosphorylase.
History of classical mechanics Medieval thought History_of_classical_mechanics > Precursors to classical mechanics > Medieval thought He also claimed that projectile in a vacuum would not stop unless it is acted upon. This conception of motion is consistent with Newton's first law of motion, inertia.
Lychrel number 196 palindrome quest Lychrel_number > 196 palindrome quest By 1 May 2006, VanLandingham had reached the 300 million digit mark (at a rate of one million digits every 5 to 7 days). Using distributed processing, in 2011 Romain Dolbeau completed a billion iterations to produce a number with 413,930,770 digits, and in February 2015 his calculations reached a number with billion digits. A palindrome has yet to be found. Other potential Lychrel numbers which have also been subjected to the same brute force method of repeated reversal addition include 879, 1997 and 7059: they have been taken to several million iterations with no palindrome being found.
Non-linear Schrödinger equation Classical equation Nonlinear_Schrödinger_equations > Equation > Classical equation The classical field equation (in dimensionless form) is: for the complex field ψ(x,t). This equation arises from the Hamiltonian H = ∫ d x {\displaystyle H=\int \mathrm {d} x\left} with the Poisson brackets { ψ ( x ) , ψ ( y ) } = { ψ ∗ ( x ) , ψ ∗ ( y ) } = 0 {\displaystyle \{\psi (x),\psi (y)\}=\{\psi ^{*}(x),\psi ^{*}(y)\}=0\,} { ψ ∗ ( x ) , ψ ( y ) } = i δ ( x − y ) . {\displaystyle \{\psi ^{*}(x),\psi (y)\}=i\delta (x-y).\,} Unlike its linear counterpart, it never describes the time evolution of a quantum state. The case with negative κ is called focusing and allows for bright soliton solutions (localized in space, and having spatial attenuation towards infinity) as well as breather solutions. It can be solved exactly by use of the inverse scattering transform, as shown by Zakharov & Shabat (1972) (see below). The other case, with κ positive, is the defocusing NLS which has dark soliton solutions (having constant amplitude at infinity, and a local spatial dip in amplitude).
Adaptive numerical differentiation Summary Numerical_differentiation In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.
First law of thermodynamics Conceptual revision: the "mechanical approach" First_law_of_thermodynamics > History > Conceptual revision: the "mechanical approach" In general, when there is transfer of energy associated with matter transfer, work and heat transfers can be distinguished only when they pass through walls physically separate from those for matter transfer. The "mechanical" approach postulates the law of conservation of energy. It also postulates that energy can be transferred from one thermodynamic system to another adiabatically as work, and that energy can be held as the internal energy of a thermodynamic system.
Alpha effect Solvent-induced effects Alpha_effect > Theory > Solvent-induced effects The alpha effect is also dependent on solvent but not in a predictable way: it can increase or decrease with solvent mix composition or even go through a maximum. At least in some cases, the alpha effect has been observed to vanish if the reaction is conducted in the gas phase, leading some to conclude that it is primarily a solvation effect. However, this explanation has limitations since similar alpha effects could be found in different solvent systems and also because the solvation affects both the basicity and the nucleophilicity of the nucleophile.
Indirect Rule Sources and references Indirect_Rule > Sources and references (Apr., 1965), pp. 267–288. R. O. Collins and J. M. Burns.
Problem solving Characteristics of complex problems Problem_solving > Characteristics of complex problems Complex problem solving (CPS) is distinguishable from simple problem solving (SPS). In SPS there is a singular and simple obstacle. In CPS there may be multiple simultaneous obstacles. For example, a surgeon at work has far more complex problems than an individual deciding what shoes to wear. As elucidated by Dietrich Dörner, and later expanded upon by Joachim Funke, complex problems have some typical characteristics, which include: complexity (large numbers of items, interrelations, and decisions) enumerability heterogeneity connectivity (hierarchy relation, communication relation, allocation relation) dynamics (time considerations)temporal constraints temporal sensitivity phase effects dynamic unpredictability intransparency (lack of clarity of the situation) commencement opacity continuation opacity polytely (multiple goals)inexpressivenes opposition transience
Lagrange equations Two-body central force problem Lagrange_equation > Examples > Two-body central force problem which is the equation of motion for a one-dimensional problem in which a particle of mass μ is subjected to the inward central force − dV/dr and a second outward force, called in this context the centrifugal force F c f = μ r θ ˙ 2 = ℓ 2 μ r 3 . {\displaystyle F_{\mathrm {cf} }=\mu r{\dot {\theta }}^{2}={\frac {\ell ^{2}}{\mu r^{3}}}\,.} Of course, if one remains entirely within the one-dimensional formulation, ℓ enters only as some imposed parameter of the external outward force, and its interpretation as angular momentum depends upon the more general two-dimensional problem from which the one-dimensional problem originated.
Animal embryonic development Summary Animal_embryonic_development The zygote undergoes mitotic divisions with no significant growth (a process known as cleavage) and cellular differentiation, leading to development of a multicellular embryo after passing through an organizational checkpoint during mid-embryogenesis. In mammals, the term refers chiefly to the early stages of prenatal development, whereas the terms fetus and fetal development describe later stages.The main stages of animal embryonic development are as follows: The zygote undergoes a series of cell divisions (called cleavage) to form a structure called a morula. The morula develops into a structure called a blastula through a process called blastulation. The blastula develops into a structure called a gastrula through a process called gastrulation. The gastrula then undergoes further development, including the formation of organs (organogenesis).The embryo then transforms into the next stage of development, the nature of which varies between different animal species (examples of possible next stages include a fetus and a larva).
Alcoholic hepatitis Pathophysiology Alcoholic_hepatitis > Pathophysiology This occurs via an increased extracellular matrix deposition around hepatocytes and sinusoidal cells which causes a peri-cellular fibrosis known as "chickenwire fibrosis". This peri-cellular chickenwire fibrosis leads to portal hypertension or an elevated blood pressure in the portal veins that drain blood from the intestines to the liver. This causes many of the sequelae of chronic liver disease including esophageal varices (with associated variceal bleeding), ascites and splenomegaly.
MHC Class II Antigen processing and presentation Class_II_MHC > Antigen processing and presentation Unlike MHC I, MHC II is meant to present extracellular pathogens rather than intracellular. Furthermore, the first step is to acquire the pathogen through phagocytosis. The pathogen is then broken down in a lysosome and a desired component is then acquired and loaded onto a MHC II molecule. The MHC II molecule then travels to the surface to present the antigen to a helper T cell. MHC II active helper T cells which help release cytokines and other things which will help induce other cells which help to combat the pathogens outside the cells.
Pi-Stacking (chemistry) Summary Aromatic_stacking_interaction In staggered stacking, one of the two aromatic rings is offset sideways so that the carbon atoms with partial negative charge in the first ring are placed above hydrogen atoms with partial positive charge in the second ring so that the electrostatic interactions become attractive. Likewise, pi-teeing interactions in which the two rings are oriented perpendicular to either other is electrostatically attractive as it places partial positively charged hydrogen atoms in close proximity to partially negatively charged carbon atoms. An alternative explanation for the preference for staggered stacking is due to the balance between van der Waals interactions (attractive dispersion plus Pauli repulsion).These staggered stacking and π-teeing interactions between aromatic rings are important in nucleobase stacking within DNA and RNA molecules, protein folding, template-directed synthesis, materials science, and molecular recognition. Despite the wide use of term pi stacking in the scientific literature, there is no theoretical justification for its use.
Felty's syndrome Neutropenia Felty's_syndrome > Mechanism > Neutropenia In Felty's syndrome, chronic activation of neutrophils progresses to neutropenia and unabated infections. Neutropenia is a decreased concentration of neutrophils in the blood. Neutrophils are the most abundant cells among white blood cells and play an important role in the immune system by destroying bacteria via phagocytosis. Inflammatory chemicals draw neutrophils to the area where they congregate and fight infection. A decrease in the number of neutrophils stimulates an autoimmune response which leads to arthritis. The loss and destruction of neutrophils leading to neutropenia are, therefore, inflammation-driven due to the body's need for an immune response.
Kalman gain Square root form Kalman_gain > Square root form One problem with the Kalman filter is its numerical stability. If the process noise covariance Qk is small, round-off error often causes a small positive eigenvalue of the state covariance matrix P to be computed as a negative number. This renders the numerical representation of P indefinite, while its true form is positive-definite. Positive definite matrices have the property that they have a triangular matrix square root P = S·ST.
Complete vector field Coordinate transformation law Gradient_vector_field > Definition > Coordinate transformation law Then the components of the vector V in the new coordinates are required to satisfy the transformation law Such a transformation law is called contravariant. A similar transformation law characterizes vector fields in physics: specifically, a vector field is a specification of n functions in each coordinate system subject to the transformation law (1) relating the different coordinate systems. Vector fields are thus contrasted with scalar fields, which associate a number or scalar to every point in space, and are also contrasted with simple lists of scalar fields, which do not transform under coordinate changes.
Quantum programming Q|SI> Quantum_programming > Quantum programming languages > Imperative languages > Q|SI> Q|SI> is a platform embedded in .Net language supporting quantum programming in a quantum extension of while-language. This platform includes a compiler of the quantum while-language and a chain of tools for the simulation of quantum computation, optimisation of quantum circuits, termination analysis of quantum programs, and verification of quantum programs.
Physical measure Origin of the risk-neutral measure Risk-neutral_measure > Origin of the risk-neutral measure It is natural to ask how a risk-neutral measure arises in a market free of arbitrage. Somehow the prices of all assets will determine a probability measure. One explanation is given by utilizing the Arrow security. For simplicity, consider a discrete (even finite) world with only one future time horizon.
History of compiler construction LL parsing History_of_compiler_construction > Context-free grammars and parsers > LL parsing LL(k) grammars can be parsed by a recursive descent parser which is usually coded by hand, although a notation such as META II might alternatively be used. The design of ALGOL sparked investigation of recursive descent, since the ALGOL language itself is recursive.
MRNA Display Method MRNA_Display > Method The in vitro translation can also be done in a PURE (protein synthesis using recombinant elements) system. PURE system is an E. coli cell-free translation system in which only essential translation components are present. Some components, such as amino acids and aminoacyl-tRNA synthases (AARSs) can be omitted from the system.
Overdiagnosis Overdiagnosis and the variability of cancer progression Overdiagnosis > Overdiagnosis and the variability of cancer progression Cancer screening is the effort to detect cancer early, during its pre-clinical phase—the time period that begins with an abnormal cell and ends when the patient notices symptoms from the cancer. It has long been known that some people have cancers with short pre-clinical phases (fast-growing, aggressive cancers), while others have cancers with long pre-clinical phases (slow-growing cancers). And this heterogeneity has an unfortunate implication: namely, screening tends to disproportionately detect slow-growing cancers (because they are accessible to be detected for a long period of time) and disproportionately miss the fast-growing cancers (because they are only accessible to be detected for a short period of time)—the very cancers we would most like to catch. For more information, see Screening (medicine)#Length time bias.
Possibility space Infinitely large sample spaces Possibility_space > Infinitely large sample spaces In an elementary approach to probability, any subset of the sample space is usually called an event. However, this gives rise to problems when the sample space is continuous, so that a more precise definition of an event is necessary. Under this definition only measurable subsets of the sample space, constituting a σ-algebra over the sample space itself, are considered events. An example of an infinitely large sample space is measuring the lifetime of a light bulb. The corresponding sample space would be [0, ∞).
Coulometric titration Karl Fischer reaction Coulometry > Applications > Karl Fischer reaction At this point in the titration, the current approaches zero. It is then possible to relate the amount of reagents used to the amount of water in the system via stoichiometry. The back-titration method is similar, but involves the addition of an excess of the reagent.
Complex fluids Dynamics Complex_fluids > Dynamics The dynamics of these systems are highly nonlinear in nature. The increase in stress by an infinitesimal amount or a small displacement of a single particle can result in the difference between an arrested state and fluid-like behavior. Although many materials found in nature can fit into the class of complex fluids, very little is well understood about them.
Depth-limited search Time complexity Iterative_deepening > Asymptotic analysis > Time complexity The time complexity of IDDFS in a (well-balanced) tree works out to be the same as breadth-first search, i.e. O ( b d ) {\displaystyle O(b^{d})} ,: 5 where b {\displaystyle b} is the branching factor and d {\displaystyle d} is the depth of the goal.
Jordan normal form Numerical analysis Jordan_normal_form > Numerical analysis If the matrix A has multiple eigenvalues, or is close to a matrix with multiple eigenvalues, then its Jordan normal form is very sensitive to perturbations. Consider for instance the matrix A = . {\displaystyle A={\begin{bmatrix}1&1\\\varepsilon &1\end{bmatrix}}.} If ε = 0, then the Jordan normal form is simply .
Aldosterone-to-renin ratio Tests Aldosterone-to-renin_ratio > Tests There is more than one way to measure the ratio. Before sampling, the patient must have a high level of blood sodium. 24-hour urinary excretion of aldosterone test: the patient eats a high-salt diet for a few days followed by urine collections over a 24-hour period sodium infusion test: the patient has a blood infusion of a salt (sodium chloride) solution a few hours before blood collection
Moduli space Moduli stacks Moduli_stack > Definitions > Moduli stacks In general, they cannot be represented by schemes or even algebraic spaces, but in many cases, they have a natural structure of an algebraic stack. Algebraic stacks and their use to analyze moduli problems appeared in Deligne-Mumford (1969) as a tool to prove the irreducibility of the (coarse) moduli space of curves of a given genus. The language of algebraic stacks essentially provides a systematic way to view the fibred category that constitutes the moduli problem as a "space", and the moduli stack of many moduli problems is better-behaved (such as smooth) than the corresponding coarse moduli space.
Multi-agent learning Definition Multi-agent_learning > Definition . , N } {\displaystyle i\in I=\{1,...,N\}} . P a → ( s , s ′ ) = Pr ( s t + 1 = s ′ ∣ s t = s , a → t = a → ) {\displaystyle P_{\overrightarrow {a}}(s,s')=\Pr(s_{t+1}=s'\mid s_{t}=s,{\overrightarrow {a}}_{t}={\overrightarrow {a}})} is the probability of transition (at time t {\displaystyle t} ) from state s {\displaystyle s} to state s ′ {\displaystyle s'} under joint action a → {\displaystyle {\overrightarrow {a}}} .
Stair riser Geometry Curved_stairs > Helical ("spiral") stairs > Geometry A "quarter-turn" stair deposits the person facing 90° from the starting orientation. Likewise, there are half-turn, three-quarters-turn and full-turn stairs. A continuous helix may make many turns depending on the height.
Feature learning Principal component analysis Feature_learning > Unsupervised > Principal component analysis In the ith iteration, the projection of the data matrix on the (i-1)th eigenvector is subtracted, and the ith singular vector is found as the right singular vector corresponding to the largest singular of the residual data matrix. PCA has several limitations. First, it assumes that the directions with large variance are of most interest, which may not be the case. PCA only relies on orthogonal transformations of the original data, and it exploits only the first- and second-order moments of the data, which may not well characterize the data distribution. Furthermore, PCA can effectively reduce dimension only when the input data vectors are correlated (which results in a few dominant eigenvalues).
Computer Arimaa Material evaluation Computer_Arimaa > Artificial intelligence techniques > Material evaluation It is important for the computer to be able to evaluate the value of the pieces on the board so it can assess whether or not a capture or exchange would be desirable. Assessing the relative value of pieces is an area of ongoing Arimaa research. Some currently used systems are DAPE and FAME.
Bayesian model of computational anatomy MAP estimation in the multiple-atlas orbit model Bayesian_model_of_computational_anatomy > MAP estimation in the multiple-atlas orbit model {\displaystyle p(I^{D}\mid I_{a})=\int _{V}p(I^{D}\mid \operatorname {Exp} _{\mathrm {id} }(v)\cdot I_{a})\pi _{V}(dv)\ .} Maximum a posteriori estimation (MAP) estimation is central to modern statistical theory. Parameters of interest θ ∈ Θ {\displaystyle \theta \in \Theta } take many forms including (i) disease type such as neurodegenerative or neurodevelopmental diseases, (ii) structure type such as cortical or subcortical structures in problems associated to segmentation of images, and (iii) template reconstruction from populations.
Bacterial sepsis Summary Bacterial_sepsis Sepsis, also known as septicemia, septicaemia, or blood poisoning, is a potentially life-threatening condition that arises when the body's response to infection causes injury to its own tissues and organs.This initial stage of sepsis is followed by suppression of the immune system. Common signs and symptoms include fever, increased heart rate, increased breathing rate, and confusion. There may also be symptoms related to a specific infection, such as a cough with pneumonia, or painful urination with a kidney infection. The very young, old, and people with a weakened immune system may have no symptoms of a specific infection, and the body temperature may be low or normal instead of having a fever.
Histone acetylation and deacetylation Summary Histone_acetylation_and_deacetylation As a consequence, the condensed chromatin is transformed into a more relaxed structure that is associated with greater levels of gene transcription. This relaxation can be reversed by deacetylation catalyzed by HDAC activity. Relaxed, transcriptionally active DNA is referred to as euchromatin. More condensed (tightly packed) DNA is referred to as heterochromatin. Condensation can be brought about by processes including deacetylation and methylation.
Rubin causal model The fundamental problem of causal inference Rubin_causal_model > An extended example > The fundamental problem of causal inference The Fundamental Problem of Causal Inference is that directly observing causal effects is impossible. However, this does not make causal inference impossible. Certain techniques and assumptions allow the fundamental problem to be overcome.
288 (number) In other areas 288_(number) > In other areas In early 20th-century molecular biology, some mysticism surrounded the use of 288 to count protein structures, largely based on the fact that it is a smooth number.A common mathematical pun involves the fact that 288 = 2 · 144, and that 144 is named as a gross: "Q: Why should the number 288 never be mentioned? A: it is two gross." == References ==
Formula In mathematics Mathematical_formula > In mathematics In mathematics, a formula generally refers to an equation relating one mathematical expression to another, with the most important ones being mathematical theorems. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius: V = 4 3 π r 3 . {\displaystyle V={\frac {4}{3}}\pi r^{3}.}
Pioneer 11 Power Pioneer_11 > Mission background > Spacecraft design > Power Pioneer 11 uses four SNAP-19 radioisotope thermoelectric generators (RTGs) (see diagram). They are positioned on two three-rod trusses, each 3 meters (9 feet 10 inches) in length and 120 degrees apart. This was expected to be a safe distance from the sensitive scientific experiments carried on board.
Information processing (psychology) Information processing model: the working memory Information_processing_(psychology) > In cognitive psychology > Models and theories > Information processing model: the working memory The storage capacity is brief but leads to an understanding of visual stimuli. Finally, there is an episodic buffer. This section is capable of taking information and putting it into long-term memory.
Process Modeling Overview Process_model > Overview One possible use of a process model is to prescribe how things must/should/could be done in contrast to the process itself which is really what happens. A process model is roughly an anticipation of what the process will look like. What the process shall be will be determined during actual system development.The goals of a process model are to be: Descriptive Track what actually happens during a process Take the point of view of an external observer who looks at the way a process has been performed and determines the improvements that must be made to make it perform more effectively or efficiently.
Velocity receiver Summary Velocity_receiver A velocity receiver (velocity sensor) is a sensor that responds to velocity rather than absolute position. For example, dynamic microphones are velocity receivers. Likewise, many electronic keyboards used for music are velocity sensitive, and may be said to possess a velocity receiver in each key.
Theory of knowledge Defining knowledge Theory_of_knowledge > Defining knowledge However, there are still various disagreements about its exact nature even though it has been studied intensely. Different factors are responsible for these disagreements. Some theorists try to furnish a practically useful definition by describing its most noteworthy and easily identifiable features.
Biological molecule Nucleosides and nucleotides Biomolecule > Nucleosides and nucleotides Both DNA and RNA are polymers, consisting of long, linear molecules assembled by polymerase enzymes from repeating structural units, or monomers, of mononucleotides. DNA uses the deoxynucleotides C, G, A, and T, while RNA uses the ribonucleotides (which have an extra hydroxyl(OH) group on the pentose ring) C, G, A, and U. Modified bases are fairly common (such as with methyl groups on the base ring), as found in ribosomal RNA or transfer RNAs or for discriminating the new from old strands of DNA after replication.Each nucleotide is made of an acyclic nitrogenous base, a pentose and one to three phosphate groups. They contain carbon, nitrogen, oxygen, hydrogen and phosphorus. They serve as sources of chemical energy (adenosine triphosphate and guanosine triphosphate), participate in cellular signaling (cyclic guanosine monophosphate and cyclic adenosine monophosphate), and are incorporated into important cofactors of enzymatic reactions (coenzyme A, flavin adenine dinucleotide, flavin mononucleotide, and nicotinamide adenine dinucleotide phosphate).
Speech and language impairment Assistive technology Speech_and_language_impairment > Management > Assistive technology Examples of unaided systems include gestures, body language, sign language, and communication boards. Communication boards are devices upon which letters, words, or pictorial symbols might be displayed; the individual may interface with the communication board to express him/herself to the other individual. Aided systems of communication do not require both individuals to be physically present in the same location, though they might be.
Cache thrashing Overview Cache_thrashing > Overview The real memory shortens its capacity to have all the pages in it, so it uses 'virtual memory'. When each page in execution demands that page that is not currently in real memory (RAM) it places some pages on virtual memory and adjusts the required page on RAM. If the CPU is too busy in doing this task, thrashing occurs.
Transformer (machine learning) Alternative functions Transformer_(neural_network) > Subsequent work > Alternative functions The original transformer uses ReLU activation function. Other activation functions were developed, such as SwiGLU.
Low-latency queuing Development Low-latency_queuing > Development Class-based weighted fair queuing (CB-WFQ) was initially released without the support of a priority queuing system, thus it could not guarantee the delay and jitter (delay variation) requirements of real-time, interactive voice and video conversations. Since for CBWFQ, the weight for a packet belonging to a specific class is derived from the bandwidth assigned to the class, which in turn determines the order in which packets are sent. All packets are serviced fairly based on weight and no class of packets may be granted strict priority. This scheme poses problems for voice traffic that is largely intolerant of delay, especially variation in delay.
Total chemical potential Summary Total_chemical_potential When both temperature and pressure are held constant, and the number of particles is expressed in moles, the chemical potential is the partial molar Gibbs free energy. At chemical equilibrium or in phase equilibrium, the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free energy is at a minimum. In a system in diffusion equilibrium, the chemical potential of any chemical species is uniformly the same everywhere throughout the system.In semiconductor physics, the chemical potential of a system of electrons at zero absolute temperature is known as the Fermi level.
Bioirrigation Summary Bioirrigation Bioirrigation refers to the process of benthic organisms flushing their burrows with overlying water. The exchange of dissolved substances between the porewater and overlying seawater that results is an important process in the context of the biogeochemistry of the oceans. Marine coastal ecosystems often have organisms that destabilize sediment. They change the physical state of the sediment.
Object categorization from image search Model Object_categorization_from_image_search > OPTIMOL > Model The two categories (target object and background) are modeled as Hierarchical Dirichlet processes (HDPs). As in the pLSA approach, it is assumed that the images can be described with the bag of words model. HDP models the distributions of an unspecified number of topics across images in a category, and across categories.
Dysosteosclerosis Neurological abnormalities Dysosteosclerosis > Symptoms and Signs > Neurological abnormalities Visual problems are often found in people with DSS. Patients experience optic atrophy due to progressive cranial nerve compression, which may lead to nystagmus or even blindness in severe cases.Other neurological abnormalities include intellectual disability, speech and psychological deterioration. Convulsions and status epilepticus are also present in patients, however the mechanisms for the development of these features are unknown. Patients also experience cranial nerve damage resulting from progressive cranial pressure.
PCI Extended PCI-X 2.0 PCI_Extended > History > PCI-X 2.0 In 2003, the PCI SIG ratified PCI-X 2.0. It adds 266-MHz and 533-MHz variants, yielding roughly 2,132 MB/s and 4,266 MB/s throughput, respectively. PCI-X 2.0 makes additional protocol revisions that are designed to help system reliability and add Error-correcting codes to the bus to avoid re-sends. To deal with one of the most common complaints of the PCI-X form factor, the 184-pin connector, 16-bit ports were developed to allow PCI-X to be used in devices with tight space constraints.